Properties

Label 128.4.b
Level $128$
Weight $4$
Character orbit 128.b
Rep. character $\chi_{128}(65,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $5$
Sturm bound $64$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(64\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(128, [\chi])\).

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

Trace form

\( 12 q - 108 q^{9} + O(q^{10}) \) \( 12 q - 108 q^{9} - 104 q^{17} - 388 q^{25} + 464 q^{33} - 552 q^{41} + 2028 q^{49} + 16 q^{57} - 416 q^{65} + 1752 q^{73} - 3332 q^{81} + 1432 q^{89} + 1624 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
128.4.b.a 128.b 8.b $2$ $7.552$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-64\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-3iq^{5}-2^{5}q^{7}-37q^{9}+\cdots\)
128.4.b.b 128.b 8.b $2$ $7.552$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+19q^{9}+5^{2}\beta q^{11}-90q^{17}+\cdots\)
128.4.b.c 128.b 8.b $2$ $7.552$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}+3^{3}q^{9}+23iq^{13}+94q^{17}+\cdots\)
128.4.b.d 128.b 8.b $2$ $7.552$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(64\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+3iq^{5}+2^{5}q^{7}-37q^{9}+\cdots\)
128.4.b.e 128.b 8.b $4$ $7.552$ \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-13q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)